Math 310/520-01/02

9-8-2017

1. Construct a truth table for .

2. Construct a truth table for .

3. Use a truth table to prove that is a
tautology. (This is called * decomposing a
conjunction*.)

Since is always true, it is a tautology.

4. In each case, determine whether the statement is true or false. Explain your answers.

(a) "If , then Calvin Butterball got a parking ticket."

(b) "If , then ."

(a) The statement " " is false. Since the if-part of the conditional is false, the conditional is true.

(b) The statement " " is true, but the statement " " is false. Hence, the conditional is false.

5. For the conditional statement "If , then the sky is blue", write the converse, the
inverse, and the contrapositive *in words*.

Converse: "If the sky is blue, then ".

Inverse: "If , then the sky isn't blue".

Contrapositive: "If the sky isn't blue, then ".

6. Use DeMorgan's Laws to * negate* each
statement, then write the negation *in words*.

(a) "Calvin buys the stromboli or Phoebe does not eat the hamburger."

(b) " is not rational and ."

(c) "If Bonzo has chicken pox, then the class will be dismissed."

(a) The negation is "Calvin does not buy the stromboli and Phoebe eats the hamburger".

(b) The negation is " is rational or ".

(c) By conditional disjuntion, the original statement is equivalent to "Bonzo does not have chicken pox or the class will be dismissed".

The negation is "Bonzo has chicken pox and the class will not be dismissed".

* [Math 520]*

7. Use a truth table to show that the following statements are logically equivalent:

The columns for and are the same, so the statements are logically equivalent.

Copyright 2017 by Bruce Ikenaga